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Stochastic Finite Element Analysis of Elastoplastic Bar Problem
Year: 2022
Type of publication: ostatní - článek ve sborníku
Name of source: Video Proceedings of Advanced Materials, Volume 3
Publisher name: International Association of Advanced Materials
Place: Ulrika
Page from-to: 267-268
Titles:
Language Name Abstract Keywords
eng Stochastic Finite Element Analysis of Elastoplastic Bar Problem From skyscrapers to stealth fighters, passing through tiny electronic components embedded in electronic devices, engineering structures are in nature very sensitive to material uncertainties. Indeed, any small defect that usually occurs due to some known or unknown reasons during the production process of a structure’s components, can in some cases be very prejudicial or even endanger the usage or functionality expected from the structure in operation. Since conventional engineering designs usually rely on a fully deterministic analysis of the problem just by considering the mean values of observed random variables, it is worth it to integrate the perturbation caused by the dispersion of random variables around its mean and investigate its repercussions on the response of the structure. That being said, this paper treats especially the stochastic finite element analysis of both linear and nonlinear elastoplastic tensile bar problems with Young’s modulus considered as a Gaussian random variable. To this end, the formulation adopted is based on the stochastic perturbation method where the expected value (stochastic displacement field) is expanded to the 10th order on the Taylor expansion series with perturbation factor. In compliance with the general stochastic perturbation-based method, the problem is firstly treaded as deterministic where the displacement field and its first derivatives are obtained successively (the predictor-implicit Backward-Euler Algorithm is employed for the incremental integration of elastoplastic models with isotropic and kinematic hardening). With the later quantities at hand, two-variable polynomial expressions of the expected value, variance and standard deviation are deduced in a straightforward manner. Finally, the study and visualisation of these statistical quantities are performed and informative notes are drawn out after comparing with the deterministic value of the displacement. The algorithms developed here have been all implemente perturbation; elastoplastic; Gaussian; stochastic; predictor-corrector

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